Question

question 14 of 28 what is the length of (overline{bc}) in the right - triangle below? a. 60 b. 17 c. 289 d. (sqrt{17})

Explanation:

Step1: Identify the Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here, if $AB = 8$ and $AC = 15$, and $BC$ is the hypotenuse.

Step2: Substitute values into the formula

Let $a = 8$ and $b = 15$. Then $BC^{2}=8^{2}+15^{2}$. Calculate $8^{2}=64$ and $15^{2}=225$. So $BC^{2}=64 + 225=289$.

Step3: Solve for $BC$

Take the square root of both sides. $BC=\sqrt{289}=17$.

Answer:

B. 17